EE

GATE Electrical Engineering 2023


Question 1
For a given vector w=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\top}, the vector normal to the plane defined by \mathbf{w}^{\top} x=1 is
A
\left[\begin{array}{lll}-2 & -2 & 2\end{array}\right]^{T}
B
\left[\begin{array}{lll}3 & 0 & -1\end{array}\right]^{T}
C
\left[\begin{array}{lll}3 & 2 & 1\end{array}\right]^{T}
D
\left[\begin{array}{llll}1 & 2 & 3\end{array}\right]^{T}
Engineering Mathematics   Calculus
Question 1 Explanation: 
Given, W^{T}=1

\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=1

We have, vector normal to the plane =\nabla F
\begin{aligned} & =i \frac{\partial F}{\partial x}+\hat{j} \frac{\partial F}{\partial y}+\hat{k} \frac{\partial F}{\partial z} \\ & =\hat{i}+2 \hat{j}+3 \hat{k} \end{aligned}

\therefore Normal vector =\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{T}
Question 2
For the block diagrm shown in the figure, the transfer function \frac{Y(s)}{R(s)} is

A
\frac{2 s+3}{s+1}
B
\frac{3 s+2}{s-1}
C
\frac{s+1}{3 \mathrm{~s}+2}
D
\frac{3 s+2}{s+1}
Control Systems   Mathematical Models of Physical Systems
Question 2 Explanation: 
Signal flow graph:

Forward paths,

\begin{aligned} & \mathrm{P}_{1}=3, \quad \Delta_{1}=1 \\ & \mathrm{P}_{2}=\frac{2}{\mathrm{~S}}, \Delta_{2}=1 \end{aligned}

Loops: L_1=\frac{1}{S}

Using Masson's graph formula,

\begin{aligned} \frac{Y(s)}{R(s)} & =\frac{P_{1} \Delta_{1}+P_{1} \Delta_{2}}{1-L_{1}} \\ & =\frac{3+\frac{2}{S}}{1-\frac{1}{S}} \\ & =\frac{3 S+2}{S-1} \end{aligned}


Question 3
In the Nyquist plot of the open-loop transfer function

\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{3 \mathrm{~s}+5}{\mathrm{~s}-1}

corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

A
\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\infty
B
\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=0
C
\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=3
D
\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=-5
Control Systems   Frequency Response Analysis
Question 3 Explanation: 
Nyquist Contour :

Given:
\begin{aligned} \mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s}) & =\frac{3 \mathrm{~s}+5}{\mathrm{~s}-1} \\ \text { Put } \quad \mathrm{s} & =R e^{j \theta} \\ \mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s}) & =\operatorname{Lim}_{R \rightarrow \infty} \frac{3 R e^{j \theta}+5}{\operatorname{Re}^{j \theta}-1} \\ \mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s}) & =3 \end{aligned}
Question 4
Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

G(s)=\frac{1}{s-1}
A
\infty, \infty
B
1,0
C
1,-1
D
-1,1
Control Systems   Feedback Characteristics of Control Systems
Question 4 Explanation: 
Given plant:

So, \quad OLTF =\frac{(3 s+1)}{s(s-1)}

Closed loop transfer function,
\begin{aligned} \frac{Y(s)}{R(s)} & =\frac{3 s+1}{s^{2}+2 s+1} \\ Y(s) & =\frac{3 s+1}{s\left(s^{2}+2 s+1\right)} \quad\left[\because R(s)=\frac{1}{s}\right] \end{aligned}

Final value of plant,
Y(\infty)=\operatorname{Lims}_{s \rightarrow 0} Y(s)=1

From plant,
\begin{aligned} X(\mathrm{~s}) & =\left[\mathrm{R}(\mathrm{s})-\frac{\mathrm{X}(\mathrm{s})}{\mathrm{s}-1}\right]\left(3+\frac{1}{\mathrm{~s}}\right) \\ X(\mathrm{~s})\left[1+\frac{3 \mathrm{~s}+1}{\mathrm{~s}(\mathrm{~s}-1)}\right] & =\left(\frac{3 \mathrm{~s}+1}{\mathrm{~s}^{2}}\right)\left[\because \mathrm{R}(\mathrm{s})=\frac{1}{\mathrm{~s}}\right] \\ X(\mathrm{~s})\left[\frac{\mathrm{s}^{2}+2 s+1}{\mathrm{~s}(\mathrm{~s}-1)}\right] & =\left(\frac{3 \mathrm{~s}+1}{\mathrm{~s}^{2}}\right) \\ \Rightarrow \quad X(\mathrm{~s}) & =\frac{(3 \mathrm{~s}+1)(\mathrm{s}-1)}{\mathrm{s}\left(\mathrm{s}^{2}+2 \mathrm{~s}+1\right)} \end{aligned}

\therefore Final value of controller,
x(\infty)=\operatorname{LimsX}_{s \rightarrow 0} \mathrm{~s}(\mathrm{~s})=-1
Question 5
The following columns present various modes of induction machine operation and the ranges of slip

\begin{array}{ll} \textbf{A (Mode of operation)}& \textbf{B (Range of slip)}\\\\ \text{a. Running in generator mode}&\text{p) From 0.0 to 1.0}\\\\ \text{b. Running in motor mode} & \text{q) From 1.0 to 2.0}\\\\ \text{c. Plugging in motor mode} & \text{r) From - 1.0 to 0.0} \end{array}
The correct matching between the elements in column A with those of column B is
A
a-r, b-p, and c-q
B
a-r, b-q, and c-p
C
a-p, b-r, and c-q
D
a-q, b-p, and c-r
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 5 Explanation: 
Torque speed characteristic of 3-\phi IM :

\mathrm{S} \gt 1 \Rightarrow Plugging mode
0 \lt \mathrm{S} \lt 1 \Rightarrow Motoring mode
\mathrm{S} \lt 0 \Rightarrow Generating Mode




There are 5 questions to complete.

GATE Electrical Engineering 2022


Question 1
The transfer function of a real system, H(s), is given as:
H(s)=\frac{As+B}{s^2+Cs+D}
where A, B, C and D are positive constants. This system cannot operate as
A
low pass filter.
B
high pass filter
C
band pass filter.
D
an integrator.
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 1 Explanation: 
Put s=0, H(0)=\frac{A \times 0+B}{0+C \times 0+D}=\frac{B}{D}
So, the system pass low frequency component. Put s=\infty , H(\infty )=0
For high pass filter, high frequency component should be non zero. Hence this system cannot be operated as high pass filter.
Question 2
For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is
A
0
B
1
C
100
D
infinite
Analog Electronics   Small Signal Analysis
Question 2 Explanation: 
For ideal MOSFET, i_G=0
Therefore, Current gain, A_I=\frac{i_s}{i_G}=\infty


Question 3
The most commonly used relay, for the protection of an alternator against loss of excitation, is
A
offset Mho relay.
B
over current relay.
C
differential relay
D
Buchholz relay.
Power Systems   Switch Gear and Protection
Question 4
The geometric mean radius of a conductor, having four equal strands with each strand of radius 'r', as shown in the figure below, is

A
4r
B
1.414r
C
2r
D
1.723r
Power Systems   Performance of Transmission Lines, Line Parameters and Corona
Question 4 Explanation: 
Redraw the configuration:

\therefore \; GMR=(r' \times 2r\times 2r\times 2\sqrt{2}r)^{1/4}
Where, r'=0.7788r
Hence, GMR=1.723r
Question 5
The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are
A
1.1, 0.15 and 0.08
B
0.15, 0.15 and 0.35
C
0.2, 0.2 and 0.2
D
0.1, 0.3 and 0.1
Power Systems   Fault Analysis
Question 5 Explanation: 
We have,
X_0 \gt X_1=X_2
(for 3-\phi transposed transmission line)




There are 5 questions to complete.

GATE Electrical Engineering 2021


Question 1
Let p and q be real numbers such that p^{2}+q^{2}=1. The eigenvalues of the matrix \begin{bmatrix} p & q\\ q& -p \end{bmatrix} are
A
1 and 1
B
1 and -1
C
j and -j
D
pq and -pq
Engineering Mathematics   Linear Algebra
Question 1 Explanation: 
Characteristic equation of A
\begin{aligned} \left|A_{2 \times 2}-\lambda I\right|&=(-1)^{2} \lambda^{2}+(-1)^{1} \text{Tr}(A) \lambda+|A|=0 \\ \lambda^{2}-(p-p) \lambda+\left(-p^{2}-q^{2}\right) &=0 \\ \Rightarrow \qquad \qquad\lambda^{2}-1 &=0 \\ \Rightarrow \qquad\qquad \lambda &=\pm 1 \end{aligned}
Question 2
Let p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3, where z is a complex number.
Which one of the following is true?
A
\text{conjugate}\:\left \{ p\left ( z \right ) \right \}=p\left ( \text{conjugate} \left \{ z \right \} \right ) for all z
B
The sum of the roots of p\left ( z \right )=0 is a real number
C
The complex roots of the equation p\left ( z \right )=0 come in conjugate pairs
D
All the roots cannot be real
Engineering Mathematics   Complex Variables
Question 2 Explanation: 
Since sum of the roots is a complex number
\Rightarrow absent one root is complex
So all the roots cannot be real.


Question 3
Let f\left ( x \right ) be a real-valued function such that {f}'\left ( x_{0} \right )=0 for some x _{0} \in\left ( 0,1 \right ), and {f}''\left ( x \right )> 0 for all x \in \left ( 0,1 \right ). Then f\left ( x \right ) has
A
no local minimum in (0,1)
B
one local maximum in (0,1)
C
exactly one local minimum in (0,1)
D
two distinct local minima in (0,1)
Engineering Mathematics   Calculus
Question 3 Explanation: 
x_{0} \in(0,1), where f(x)=0 is stationary point
and f^{\prime \prime}(x)>0 \qquad \qquad \forall x \in(0,1)
So \qquad \qquad f^{\prime}\left(x_{0}\right)=0
and \qquad \qquad f^{\prime}(0)>0, \text { where } x_{0} \in(0,1)
Hence, f(x) has exactly one local minima in (0,1)
Question 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals 'ab' is

A
\text{10 V} in series with 12\:\Omega
B
\text{65 V} in series with 15\:\Omega
C
\text{50 V} in series with 2\:\Omega
D
\text{35 V} in series with 2\:\Omega
Electric Circuits   Network Theorems
Question 4 Explanation: 
Given circuit can be resolved as shown below,


V_{T H}=15+50=65 \mathrm{~V}


\begin{aligned} V_{x} &=2+3+10=15 \mathrm{~V} \\ R_{\mathrm{TH}} &=\frac{V_{x}}{1}=15 \Omega \end{aligned}
Question 5
Which one of the following vector functions represents a magnetic field \overrightarrow{B}?
(\hat{X}, \hat{Y} and \hat{Z} are unit vectors along x-axis, y-axis, and z-axis, respectively)
A
10x\hat{X}+20y\hat{Y}-30z\hat{Z}
B
10y\hat{X}+20x\hat{Y}-10z\hat{Z}
C
10z\hat{X}+20y\hat{Y}-30x\hat{Z}
D
10x\hat{X}-30z\hat{Y}+20y\hat{Z}
Electromagnetic Theory   Magnetostatic Fields
Question 5 Explanation: 
If \vec{B} is magnetic flux density then \vec{\nabla} \cdot \vec{B}=0
\begin{aligned} &\vec{\nabla} \cdot \vec{B}=\frac{\partial B x}{\partial x}+\frac{\partial B y}{\partial y}+\frac{\partial B z}{\partial z}\\ &\frac{\partial}{\partial x}(10 x)+\frac{\partial}{\partial y}(20 y)+\frac{\partial}{\partial z}(-30 z)=\vec{\nabla} \cdot \vec{B}\\ &\qquad \qquad \vec{\nabla} \cdot \vec{B}=10+20-30=0 \end{aligned}




There are 5 questions to complete.

GATE Notes – Electrical Engineering

GATE Electrical Engineering notes for all subjects as per syllabus of GATE 2024 Electrical Engineering.






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Prepare for GATE 2024 with practice of GATE Electrical previous year questions and solution

Practice of GATE Electrical Engineering previous year questions is an effective approach for candidates preparing for the GATE 2024 Electrical Engineering examination. This approach involves practicing previous year question papers topic-wise to develop a strong understanding of the fundamental concepts and their application.

Candidates should attempt as many previous year question papers topic-wise as possible to increase their Rank in the GATE 2024 Electrical Engineering examination and securing admission to their dream postgraduate program

Power Electronics Miscellaneous


Question 1
A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diode. D, represented approximately as a piecewise linear plot of current vs time at diode turn-off. L_{par} is a parasitic inductance due to the wiring of the circuit, and is in series with the diode. The point on the plot (indicate your choice by entering 1. 2, 3 or 4) at which the IGBT experiences the highest current stress is ______.
A
1
B
2
C
3
D
4
GATE EE 2020   Power Electronics
Question 1 Explanation: 


Using KCL, I_s=I_L-I_D
For inductively loaded circuits, load can be assumed to be constant.
\therefore \; I_s is maximum when, I_D is minimum, i.e. at point 3.
Therefore, IGBT experiences highest current stress at point 3.
Question 2
For the circuit shown in the figure below, assume that diodes D_1,D_2 and D_3 are ideal.

The DC components of voltages v_1 \; and \; v_2, respectively are
A
0 V and 1 V
B
-0.5 V and 0.5 V
C
1 V and 0.5 V
D
1 V and 1 V
GATE EE 2017-SET-1   Power Electronics
Question 2 Explanation: 


\begin{aligned} V_{2\; avg}&=\frac{V_m}{\pi}=\frac{\pi/2}{\pi}=\frac{1}{2}=0.5V \\ V_{1\; avg} &=\frac{1}{2 \pi}[ \int_{0}^{\pi}\frac{\pi}{2}\sin 100 \pi t\cdot d(\omega t)\\ &+\int_{\pi}^{2\pi} \pi \sin 100 \pi t\cdot d(\omega t) ]\\ &= -0.5V \end{aligned}


Question 3
Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current, are given by: V_{1}=500 kV, V_{2}=485 kV and V_{3}=1.5 kA. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations is feasible?
A
V_{1}=-500 kV,V_{2}=-485 kV and latex]I=1.5kA[/latex]
B
V_{1}=-485 kV,V_{2}=500 kV and latex]I=1.5kA[/latex]
C
V_{1}=500 kV,V_{2}=-485 kV and latex]I=-1.5kA[/latex]
D
V_{1}=-500 kV,V_{2}=-485 kV and latex]I=-1.5kA[/latex]
GATE EE 2015-SET-1   Power Electronics
Question 3 Explanation: 
To maintain the direction of power flow from system 2 to system 1, the voltage V_1=-485kV and voltage V_2=500kV and I=1.5kA.
Since, current cannot flow in reverse direction. Option (B) is correct answer.
Question 4
The SCR in the circuit shown has a latching current of 40 mA. A gate pulse of 50 \mus is applied to the SCR. The maximum value of R in \Omega to ensure successful firing of the SCR is ______.
A
4050
B
5560
C
6060
D
8015
GATE EE 2014-SET-2   Power Electronics
Question 4 Explanation: 
Let us assume the SCR is conducting,

\begin{aligned} &I_{ss}=\frac{100}{500}=0.2A\\ &[\because \text{inductor will be dhort circuited in DC}]\\ &i(t)=I_{ss}(1-e^{-t/\tau })\\ &\tau =\frac{L}{R}=\frac{200 \times 10^{-3}}{500}\\ &\;\;=4 \times 10^{-4}\; sec\\ &\text{Given }t=50 \times 10^{-6}\; sec\\ &\therefore \; i(t)=0.2\left ( 1-e^{\frac{50 \times 10^{-6}}{4 \times 10^{-4}}} \right )=23.5A \end{aligned}

V=I \times R
R=\frac{V}{I}=\frac{100}{16.5 \times 10^{-3}} =6060 \Omega
Question 5
A single-phase SCR based ac regulator is feeding power to a load consisting of 5 \Omega resistance and 16 mH inductance. The input supply is 230 V, 50 Hz ac. The maximum firing angle at which the voltage across the device becomes zero all throughout and the rms value of current through SCR, under this operating condition, are
A
30^{\circ} and 46 A
B
30^{\circ} and 23 A
C
45^{\circ} and 23 A
D
45^{\circ} and 32 A
GATE EE 2014-SET-2   Power Electronics
Question 5 Explanation: 
The maximum firing angle at which the voltage across the device becomes '\phi ' = load angle.
\begin{aligned} \phi &= \tan ^{-1} \left ( \frac{\omega L}{R} \right )\\ &= \tan^{-1}\left ( \frac{2 \pi \times 50 \times 16 \times 10^{-3}}{5} \right ) \\ \phi &=45.15\simeq 45^{\circ} \end{aligned}
Rms value of current through SCR is
\begin{aligned} I_{T_{rms}} &=\sqrt{\left [ \frac{1}{2 \pi}\int_{\alpha }^{\pi+\alpha }\left ( \frac{V_m}{z}\sin (\omega t-\phi ) \right )^2 d(\omega t) \right ]}\\ &=\sqrt{\frac{V_m^2}{2 \pi z^2} \int_{\alpha }^{\pi+\alpha } \left [ \frac{1-\cos 2(\omega t-\phi )}{2} \right ] d(\omega t)}\\ &=\sqrt{\frac{V_m^2}{2 \times 2 \pi z^2} \left [\pi- \left.\begin{matrix} \frac{\sin 2(\omega t-\phi )}{2} \end{matrix}\right|_\alpha ^{(\pi+\alpha )} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} } \sqrt{\left [ \pi+\frac{-\sin 2(\pi+\alpha -\alpha )+\sin 2(\alpha -\alpha )}{2} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} }\sqrt{\pi}=\frac{V_m}{2z}\\ I_{T_{rms}}&=\frac{230\sqrt{2}}{2 \times \sqrt{5^2(2 \pi \times 50 \times 16 \times 10^{-3})^2}}\\ &=22.93\simeq 23A\\ I_{T_{rms}}&=23A \end{aligned}


There are 5 questions to complete.

GATE Electrical Engineering-Topic wise Previous Year Questions

Prepare for GATE 2024 with practice of GATE Electrical previous year questions and solution

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Prepare for GATE 2024 with practice of GATE Electrical previous year questions and solution

Topic-wise practice of GATE Electrical Engineering previous year questions is an effective approach for candidates preparing for the GATE 2024 Electrical Engineering examination. This approach involves practicing previous year question papers topic-wise to develop a strong understanding of the fundamental concepts and their application.

Candidates should attempt as many previous year question papers topic-wise as possible to increase their Rank in the GATE 2024 Electrical Engineeringexamination and securing admission to their dream postgraduate program

GATE 2024 Electrical Engineering Syllabus


Revised syllabus of GATE 2024 Electrical Engineering by IIT.

Practice GATE Electrical Engineering previous year questions

Year wise | Subject wise | Topic wise

Section 1: Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Divergence theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
Section 2: Electric circuits

Network elements: ideal voltage and current sources, dependent sources, R, L, C, M elements; Network solution methods: KCL, KVL, Node and Mesh analysis; Network Theorems: Thevenin’s, Norton’s, Superposition and Maximum Power Transfer theorem; Transient response of dc and ac networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in ac circuits.
Section 3: Electromagnetic Fields

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.
Section 4: Signals and Systems

Representation of continuous and discrete time signals, shifting and scaling properties, linear time invariant and
causal systems, Fourier series representation of continuous and discrete time periodic signals, sampling theorem,
Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform.
Section 5: Electrical Machines

Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and
efficiency;
Three-phase transformers: connections, vector groups, parallel operation; Auto-transformer, Electromechanical energy conversion principles;
DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors;
Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control; Operating principle of single-phase induction motors;
Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors; Types of losses and efficiency calculations of electric machines
Section 6: Power Systems

Basic concepts of electrical power generation, ac and dc transmission concepts, Models and performance of transmission lines and cables, Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, Gauss- Seidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power factor correction, Symmetrical components, Symmetrical and unsymmetrical fault analysis, Principles of over‐current, differential, directional and distance protection; Circuit breakers, System stability concepts, Equal area criterion, Economic Load Dispatch (with and without considering transmission losses).
Section 7: Control Systems

Mathematical modeling and representation of systems, Feedback principle, transfer function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of linear time invariant systems, Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State space model, Solution of state equations of LTI systems, R.M.S. value, average value calculation for any general periodic waveform.
Section 8: Electrical and Electronic Measurements

Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, Error analysis.
Section 9: Analog Electronics and Digital Electronics

Simple diode circuits: clipping, clamping, rectifiers; Amplifiers: biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers: characteristics and applications; single stage active filters, Sallen Key, Butterworth, VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers, Schmitt triggers, sample and hold circuits, A/D and D/A converters.
Section 10: Power Electronics

Static V-I characteristics and firing/gating circuits for Thyristor, MOSFET, IGBT; DC to DC conversion: Buck, Boost and Buck-Boost Converters; Single and three-phase configuration of uncontrolled rectifiers; Voltage and Current commutated Thyristor based converters; Bidirectional ac to dc voltage source converters; Magnitude and Phase of line current harmonics for uncontrolled and thyristor based converters; Power factor and Distortion Factor of ac to dc converters; Single-phase and three-phase voltage and current source inverters, sinusoidal pulse width modulation.

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GATE EE 2014 SET 2


Question 1
Which one of the following statements is true for all real symmetric matrices?
A
All the eigenvalues are real.
B
All the eigenvalues are positive.
C
All the eigenvalues are distinct.
D
Sum of all the eigenvalues is zero.
Engineering Mathematics   Linear Algebra
Question 2
Consider a dice with the property that the probability of a face with n dots showing up proportional to n. The probability of the face with three dots showing up is____.
A
0.1
B
0.33
C
0.14
D
0.66
Engineering Mathematics   Probability and Statistics
Question 2 Explanation: 
Let probability of occurence of one dot is P.
So, writing total probability
P+2P+3P+4P+5P+6P=1
P=\frac{1}{21}
Hence, problem of occurrence of 3 dot is =3P=\frac{3}{21}=\frac{1}{7}=0.142


Question 3
Minimum of the real valued function f(x)=(x-1)^{2/3} occurs at x equal to
A
-\infty
B
0
C
1
D
\infty
Engineering Mathematics   Calculus
Question 3 Explanation: 
f(x)=(x-1)^{2/3}=(\sqrt[3]{x-1})^2
As f(x) is square of \sqrt[3]{x-1}, hence its minimum value be 0 where at x=1.
Question 4
All the values of the multi-valued complex function 1^i, where i=\sqrt{-1}, are
A
purely imaginary
B
real and non-negative
C
on the unit circle
D
equal in real and imaginary parts
Engineering Mathematics   Complex Variables
Question 4 Explanation: 
Let z=1^i=1^{e^{i(4n+1)\pi/2}}\;\;\;n \in I
z=1 which is purly real and non negative.
Question 5
Consider the differential equation x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-y=0. Which of the following is a solution to this differential equation for x \gt 0 ?
A
e^{x}
B
x^{2}
C
1/x
D
ln x
Engineering Mathematics   Differential Equations
Question 5 Explanation: 
\begin{aligned} x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y&=0\\ \text{Let, }x=e^z\leftrightarrow z&=\log x\\ s\frac{d}{dx}=xD=\theta &=\frac{d}{dz}\\ x^2D^2&=\theta (\theta -1)\\ (x^2D^2+xD-1)y&=0\\ [\theta (\theta -1)+\theta -1]y&=0\\ (\theta ^2-\theta +\theta -1)&=0\\ (\theta ^2-1)y&=0\\ \text{Auxiliary equation is }m^2-1&=0\\ m&=\pm 1\\ \text{CF is }C_1e^{-z}+C_2e^z&\\ \text{Solution is }y&=C_1e^{-z}+C_2e^z\\ y&=C_1x^{-1}+C_2x\\ y&=C_1\frac{1}{x}+C_2x \end{aligned}
One independent solution is \frac{1}{x}
Another independent solution is x.




There are 5 questions to complete.

GATE EE 2014 SET 3


Question 1
Two matrices A and B are given below:
A=\begin{bmatrix} p &q \\ r& s \end{bmatrix}; B=\begin{bmatrix} p^2+q^2 & pr +qs \\ pr+qs & r^2+s^2 \end{bmatrix}
If the rank of matrix A is N, then the rank of matrix B is
A
N/2
B
N-1
C
N
D
2N
Engineering Mathematics   Linear Algebra
Question 1 Explanation: 
\begin{aligned} A &=\begin{bmatrix} p & q\\ r & s \end{bmatrix} \\ A \times A=A^2&=\begin{bmatrix} p^2+q^2 & pr+qs\\ pr+qs & r^2+s^2 \end{bmatrix} =B \\ A^2 &=B \end{aligned}
Rank of amtrix does not change when we squaring the matrix, hence rank of B = rank of A=N.
Question 2
A particle, starting from origin at t=0s, is traveling along x-axis with velocity
v=\frac{\pi}{2}\cos (\frac{\pi}{2}t)m/s
At t=3s, the difference between the distance covered by the particle and the magnitude of displacement from the origin is_____
A
1
B
2
C
3
D
4
Engineering Mathematics   Calculus


Question 3
Let \triangledown \cdot (f v)=x^2y+y^2z+z^2x, where f and v are scalar and vector fields respectively. If v=yi+zj+xk , then v\cdot \triangledown f is
A
x^2y+y^2z+z^2x
B
2xy+2yz+2zx
C
x+y+z
D
0
Engineering Mathematics   Calculus
Question 3 Explanation: 
\begin{aligned} \vec{V}&=y\hat{i}+z\hat{j}+x\hat{k}\\ \hat{i}\frac{\partial (fV)}{\partial x}+\hat{j}\frac{\partial (fV)}{\partial y}+\hat{k}\frac{\partial (fV)}{\partial z}&=x^2y+y^2z+z^2x\\ y\frac{\partial f}{\partial x}+z\frac{\partial f}{\partial y}+x\frac{\partial f}{\partial z}&=x^2y+y^2z+z^2x\;\;...(i)\\ \vec{V}\cdot \Delta f&=y\frac{\partial f}{\partial x}+z\frac{\partial f}{\partial y}+x\frac{\partial f}{\partial z}\;\;...(ii)\\ \text{From equations (i) and (ii)}\\ \vec{V}\cdot \Delta f&=x^2y+y^2z+z^2x \end{aligned}
Question 4
Lifetime of an electric bulb is a random variable with density f(x)=kx^2, where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is _____
A
0.85
B
0.42
C
0.25
D
0.75
Engineering Mathematics   Probability and Statistics
Question 4 Explanation: 
Life time of an electric bulb with density
f(x)=Kx^2
If minimum and maximum lifetimes of bulb are 1 and 2 years respectively then
\begin{aligned} \int_{1}^{2}Kx^2dx &=1\\ \left.\begin{matrix} K\frac{x^3}{3} \end{matrix}\right|_1^2&=1\\ K\left ( \frac{8}{3}-\frac{1}{3} \right )&=1\\ \frac{7K}{3}&=1\\ K&=\frac{3}{7}=0.42 \end{aligned}
Question 5
A function f(t) is shown in the figure.

The Fourier transform F(\omega) of f(t) is
A
real and even function of w
B
real and odd function of w
C
imaginary and odd function of w
D
imaginary and even function of w
Signals and Systems   Fourier Transform
Question 5 Explanation: 
Fiven signal f(t) is an odd signal. Hence, F(\omega ) is imaginary and odd function of \omega .




There are 5 questions to complete.

GATE EE 2015 SET 1


Question 1
A random variable X has probability density function f(x) as given below:

f(x)=\left\{\begin{matrix} a+bx & for \; 0 \lt x \lt 1\\ 0& otherwise \end{matrix}\right.

If the expected value E[X]=2/3, then Pr[X \lt 0.5] is _____________.
A
0.25
B
0.5
C
0.75
D
1
Engineering Mathematics   Probability and Statistics
Question 1 Explanation: 
\begin{aligned} f(x)&=\left\{\begin{matrix} a+bx & \text{for }0 \lt x \lt 1\\ 0 & \text{otherwise} \end{matrix}\right.&\\ \text{Now given }E(X)&=2/3\\ \int_{0}^{1}xf(x)dx&=\frac{2}{3}\\ \int_{0}^{1}x(a+bx)dx&=\frac{2}{3}\\ a\left ( \frac{x^2}{2} \right )_0^1+b\left ( \frac{x^3}{3} \right )_0^1&=\frac{2}{3}\\ a\left ( \frac{1}{2} \right )+b\left ( \frac{1}{3} \right )&=\frac{2}{3}\\ 3a+2b&=4\;\;...(i)\\ \text{Now, }\int_{0}^{1}f(x)dx &=1\\ (\text{total probability} & \text{ is always equal to 1})\\ \int_{0}^{1}(a+bx)dx&=\left ( ax+\frac{bx^2}{2} \right )_0^1=1\\ a+\frac{b}{2}&=1\\ 2a+b&=2\;\;...(ii)\\ \text{Now solving } & \text{ (i) and (ii), we get}\\ a&=0,b=2\\ So,\; \;f(x)&=\left\{\begin{matrix} 2x & \text{for }0 \lt x lt 1\\ 0 & \text{otherwise} \end{matrix}\right.&\\ \text{Now we need}&\\ P(x \lt 0.5)&=\int_{0}^{0.5}2xdx=2\left ( \frac{x^2}{2} \right )_0^{0.5}\\ &=0.5^2-0^2=0.25 \end{aligned}
Question 2
If a continuous function f(x) does not have a root in the interval [a,b], then which one of the following statements is TRUE?
A
f(a)\cdot f(b)=0
B
f(a)\cdot f(b) \lt 0
C
f(a)\cdot f(b) \gt 0
D
f(a)/ f(b)\leq 0
Engineering Mathematics   Calculus
Question 2 Explanation: 
Intermediate value theorem states that if a function is continious and f(a) \cdot f(b) \lt 0, then surely there is a root in (a,b). The contrapositive of this theorem is that if a function is continious and has no root in (a,b) then surely f(a) \cdot f(b) \geq 0. But since it is given that there is no root in the closed interval [a,b] it means f(a) \cdot f(b) \neq 0.
So surely f(a) \cdot f(b) \gt 0 which is choise(C).


Question 3
If the sum of the diagonal elements of a 2x2 matrix is -6, then the maximum possible value of determinant of the matrix is ________.
A
6
B
8
C
9
D
12
Engineering Mathematics   Linear Algebra
Question 3 Explanation: 
Consider a symmetric matrix A =\begin{bmatrix} a & b\\ b & d \end{bmatrix}
Given a+d=-6
|A|=ad-b^2
Now since b^2 is always non-negative, maximum determinant will come when b^2=0.
So we need to maximize
\begin{aligned} |A|&=ad-0=ad=a \times -(6+a) \\ &= -a^2-6a\\ \frac{d|A|}{da} &=-2a-6=0 \\ \Rightarrow \;\; a &=-3 \text{ is the only stationary point} \end{aligned}
Since, \left [\frac{d^2|A|}{da} \right ]_{a=-3}=-2 \lt 0, we have a maximum at a=-3.
Since a+d=-6, corresponding value of d=-3.
|A|=ad=-3 \times -3=9
Question 4
Consider a function \vec{f}=\frac{1}{r^{2}}\hat{r}, where r is the distance from the origin and \hat{r} is the unit vector in the radial direction. The divergence of this function over a sphere of radius R, which includes the origin, is
A
0
B
2\pi
C
4\pi
D
R\pi
Electromagnetic Fields   Coordinate Systems and Vector Calculus
Question 4 Explanation: 
\bar{f}=\frac{1}{r^2}\hat{r}
From divergence theorem as we know,
\begin{aligned} \int _{vol.} (\triangledown \cdot \bar{f})dV &=\oint \oint _S \bar{f}\cdot d\bar{S}\\ \oint \oint _S \bar{f}\cdot d\bar{S} &= \oint \oint _S \left ( \frac{1}{r^2} \cdot \hat{r}\right ) \times r^2 \sin \theta \cdot d\theta \cdot d\phi \cdot \hat{r} \\ &= \oint \oint _S \sin \theta \cdot d\theta \cdot d\phi=4\pi \end{aligned}
Question 5
When the Wheatstone bridge shown in the figure is used to find the value of resistor R_X, the galvanometer G indicates zero current when R_1=50\Omega ,R_2=65\Omega and R_3=100\Omega. If R_3 is known with \pm 5% tolerance on its nominal value of 100 \Omega , what is the range of R_X in Ohms?
A
[123.50, 136.50]
B
[125.89, 134.12]
C
[117.00, 143.00]
D
[120.25, 139.75]
Electrical and Electronic Measurements   Characteristics of Instruments and Measurement Systems
Question 5 Explanation: 
R_1=50\Omega
R_2=60\Omega
R_3=100\pm 5%\Omega
The value of R_3 \text{with} \pm 5% of tollerance,
\begin{aligned} R_3&= 100\pm 5\% \\ &= 100+100 \times \frac{5}{100}=105 \Omega \\ &= 100-100 \times \frac{5}{100}=95 \Omega \end{aligned}
In both condition, the bridge is balance, so under balance condition,
\begin{aligned} \frac{R_1}{R_3}&=\frac{R_2}{R_x} \\ R_x&=\frac{R_2R_3}{R_1} \\ (i) \; \text{when}, \; R_3&=105\Omega \\ \therefore \;\;R_x &= \frac{105 \times 65}{50}=136.50\Omega \\ (ii)\; \text{when}, \; R_3&=95 \Omega \\ \therefore \;\;R_x &= \frac{95 \times 65}{50}=123.50\Omega \end{aligned}




There are 5 questions to complete.